ITS Berkeley

An Investigation of the Accuracy of the Clark Approximation for the Multinomial Probit Model

Horowitz, Joel L.
Sparmann, Jürg M.
Carlos Daganzo
1982

The Clark approximation, in which the maximum of two normally distributed random variables is approximated by a third normally distributed random variable, forms the basis of a relatively inexpensive technique for evaluating the choice probabilities of multinomial probit models. This paper reports the results of a series of numerical experiments in which the accuracy of probit computations based on the Clark approximation was investigated. In contrast to previous investigations, these experiments dealt with the accuracy of the results obtained when the Clark approximation is used for...

Multinomial Probit with Time-Series Data: Unifying State Dependence and Serial Correlation Models

Carlos Daganzo
Sheffi, Y.
1982

This paper develops a general method for treating discrete data sets containing individuals that have made more than one choice under varying stimuli. The multinomial probit model is shown to possess properties that make it very attractive for this application, as with it, it is possible to develop an estimation process that uses all the information in the data, and is both relatively inexpensive and consistent with utility maximization. The method, which is a generalization of Heckman's binary model, can include taste variations and more than two alternatives.

Tandem Toll Booths for the Golden Gate Bridge

Hall, Randolph W.
Carlos Daganzo
1983

Many toll plazas are constrained in width by buildings or other physical barriers. These barriers may make the cost of adding toll lanes prohibitive. One method for increasing the capacity of a toll facility without increasing its width is to use tandem toll booths. A tandem toll booth consists of two toll takers in a single toll lane both serving alternating sets of vehicles simultaneously. The capacity of tandem toll booths is calculated with time-space diagrams and the cumulative headway distributions of vehicles at a conventional toll booth. The capacity depends on the maximum of...

Unconstrained Extremal Formulation of Some Transportation Equilibrium Problems

Carlos Daganzo
1982

This paper presents transportation equilibrium results that apply to both discrete choice models and network problems. Specifically, it shows that many network equilibrium problems admit an unconstrained extremal formulation and that unconstrained optimization algorithms may be used for their solution. Similar results are derived for equilibrium problems involving discrete choice models. It also shows that a certain class of stochastic networks exhibit unique equilibria and that simulation algorithms with fixed step sizes converge almost surely to the equilibrium point.

Railroad Classification Yard Throughput: The Case of Multistage Triangular Sorting

Carlos Daganzo
Dowling, Richard G.
Hall, Randolph W.
1983

Procedures for improving the efficiency of classification yard operations are studied in this paper. Multistage sorting strategies make efficient use of land and tracks. Equations are derived giving the service time per car and space requirements of three multistage sorting strategies: the sorting-by-block, the sorting-by-train, and the triangular sorting strategies. Exact service time formulas are given for the first two strategies, and an approximation is given for the last strategy. The approximation, when compared with exact calculations, proved to be quite robust. Errors were on the...

On the Estimation of the Multinomial Probit Model

Sheffi, Yosef
Hall, Randy
Carlos Daganzo
1982

Multinomial Probit provides, perhaps, the most satisfactory form of discrete choice model based on the framework of utility maximization. It has clear advantages over more commonly used alternatives, such as the multinomial logit model, although its use involves more computational effort. This paper discusses the problems both of calculating the multinomial probit choice functions and in estimating the model parameters. Four techniques for calculating the choice functions are reviewed with regard to their comparative accuracy, computational requirements and applicability. With regard to...

The Role of Break Bulk Terminals in Many to Many Logistic Networks

Carlos Daganzo
1984

Design of Multiple Vehicle Delivery Tours

Newell, G. F.
Carlos Daganzo
1984

Stochastic Network Equilibrium with Multiple Vehicle Types and Asymmetric, Indefinite Link Cost Jacobians

Carlos Daganzo
1983

This paper discusses a family of general link cost functions that can be used to model multimodal transportation network equilibrium problems. The family includes as a special case the currently favored family of monotonically increasing functions but does not necessarily have to have a symmetric or semi-definite Jacobian. In this way multimodal networks can be modeled somewhat more realistically. The paper also allows stochastic link costs for some or all the links and modes. It is shown that under mild conditions the equilibrium exists and is unique, but more importantly, that there is a...

Derivation of Delays Based on Input-Output Analysis

Carlos Daganzo
1983

In a recent paper Michalpoulos and Pisharody (1981) contend that traditional input-output analysis results in substantial overestimation of delays, and they develop an alternate, more laborious, calculation method. This premise is incorrect since input-output analysis is nothing more than a simple accounting method, which by definition gives exact results. It should give results consistent with the more laborious method proposed by those authors.